1. Field of The Invention
The present invention relates to a position detecting method, an optical characteristic measuring method and unit, an exposure apparatus, and a device manufacturing method, and more specifically to a position detecting method for detecting the positions of a plurality of features in an image formed on the image plane of an optical system, an optical characteristic measuring method and unit for measuring an optical characteristic of an optical system to be examined using the position detecting method, an exposure apparatus comprising the optical characteristic measuring unit, and a device manufacturing method using the exposure apparatus.
2. Description of The Related Art
In a lithography process for manufacturing semiconductor devices, liquid crystal display devices, or the like, exposure apparatuses have been used which transfer a pattern (also referred to as a xe2x80x9creticle patternxe2x80x9d hereinafter) formed on a mask or reticle (generically referred to as a xe2x80x9creticlexe2x80x9d hereinafter) onto a substrate, such as a wafer or glass plate (hereinafter, generically referred to as a xe2x80x9csubstratexe2x80x9d as needed), coated with a resist through a projection optical system. As such an exposure apparatus, a stationary-exposure-type projection exposure apparatus such as the so-called stepper, or a scanning-exposure-type projection exposure apparatus such as the so-called scanning stepper is mainly used.
Such an exposure apparatus needs to accurately project the pattern on a reticle onto a substrate with high resolving power. Therefore, the projection optical system is designed to have a good optical characteristic with various types of aberrations being reduced.
However, it is difficult to make a projection optical system completely as is planned in design, and various types of aberrations due to various factors remain in a projection optical system actually made. Therefore, the optical characteristic of the projection optical system actually made is not the same as planned in design.
Various technologies for measuring the optical characteristic, related to aberration, of the actually made projection optical system as an optical system to be examined have been suggested, and of those technologies a wave-front aberration measuring method is attracting attentions, which comprises (a) making a spherical wave produced by a pinhole incident on the optical system to be examined, (b) producing parallel rays of light from light that has passed through the optical system to be examined and forms a pinhole image and dividing the wave front thereof into a plurality of portions, (c) making each of the portions (hereinafter, called xe2x80x9cdivided wave-front portionsxe2x80x9d) form a spot image, and (d) calculating wave-front aberration due to the optical system based on measured positions where the spot images are formed.
A wave-front aberration measuring unit using this method may comprise a micro-lens array, in which a plurality of micro lenses are arranged along a two-dimensional plane parallel to the ideal wave front of the parallel rays of light, as a wave-front dividing device for dividing the incident light and making each of the divided wave-front portions form a spot image. The wave-front aberration measuring unit picks up the spot images by a pick-up device such as CCD and calculates wave-front aberration based on deviations of the spot images"" positions, which are detected from the pick-up result, from positions planned in design.
Since such a wave-front aberration measuring unit with the micro-lens array can pick up the spot images formed by the divided wave-front portions at one time, the unit is excellent in terms of quickly measuring wave front aberration.
As a premise of measuring wave front aberration, the tilts of the divided wave-front portions, if any, can be considered linear. Therefore, the wave front is preferably divided into as small portions as possible in order to accurately measure the wave front aberration.
However, as the divided wave-front portions become smaller, the distances between the spot images formed through the micro lenses of the micro-lens array become short. As a result, in view of the whole image including the spot images the position of the spot image formed through a micro lens is influenced by the spot images formed through its neighboring micro lenses. That is, cross-talks between spot images, especially between spot images adjacent to each other, are not negligible, which cause the shapes of the spot images to be distorted relative to the original shape thereof, so that the positions of the spot images obtained from the pick-up result are displaced from the real positions thereof by their respective neighboring spot images.
When spot images near a given spot image are symmetrically arranged around the given spot image, the influences from the neighboring spot images cancel each other, so that the displacement of the given spot image does not occur. Meanwhile, when spot images near a given spot image are asymmetrically arranged around the given spot image, the influences from the neighboring spot images do not cancel each other, and at least parts of the influences remain, so that the given spot image is displaced. Therefore, when spot images near a given spot image are asymmetrically arranged around the given spot image, the accuracy in detecting the real position of the given spot image decreases. Especially, no spot image exists on one side in a specific direction of a spot image present in the periphery of the whole image corresponding to the periphery of the pupil, so that the asymmetry of the arrangement of spot images is large in the periphery. Therefore, the accuracy in detecting positions of such a spot image is affected to a great extent with causing the measurement accuracy in measuring wave front aberration to decrease.
This invention was made under such circumstances, and a first purpose of the present invention is to provide a position detecting method which can accurately detect the real positions of a plurality of features even when cross-talks are present between the plurality of features formed on the image plane.
Moreover, a second purpose of the present invention is to provide an optical characteristic measuring method and unit which accurately detects the optical characteristic of an optical system to be examined.
Furthermore, a third purpose of the present invention is to provide an exposure apparatus that can accurately transfer a given pattern onto a substrate.
Moreover, a fourth purpose of the present invention is to provide a device manufacturing method which can manufacture highly integrated devices having a fine pattern thereon.
According to knowledge obtained from the study by the inventor of this invention, it is possible to make an optical system including the micro-lens array, which is used for measuring wave front aberration, as planned in design, and when the optical system is made as planned in design, the whole image data on the image plane when real spot images are assumed to be present in estimated positions can be accurately calculated based on the optical model of the optical system, in which whole image data spot images assumed to be present in the estimated positions are superposed. This invention was made on the basis of such knowledge.
According to a first aspect of the present invention, there is provided a position detecting method with which to detect positions of a plurality of features in an image formed on an image plane by a predetermined optical system, the position detecting method comprising calculating initial estimated feature positions of the plurality of features using a specific algorism based on the image formed on the image plane; calculating image information on the image plane using a model for the predetermined optical system in view of the features being formed in respective current estimated feature positions; calculating comparison feature positions using the specific algorism based on the image information; correcting the current estimated feature positions by amounts corresponding to differences between the initial estimated feature positions and the comparison feature positions, so that the current estimated feature positions are updated; and repeating the calculating of image information, the calculating of comparison feature positions, and the correcting and updating of the current estimated feature positions.
According to this, initial estimated feature positions are calculated using a specific algorism, and are set as current estimated feature positions. Subsequently, image information on the image plane is calculated using a predetermined optical model and assuming the current estimated feature positions to be real feature positions, and comparison feature positions are calculated using the specific algorism and assuming that an image calculated based on the image information is formed on the image plane.
The differences between the initial estimated feature positions and the comparison feature positions are approximations of the differences between the current estimated feature positions and the real feature positions, and if the differences between the initial estimated feature positions and the comparison feature positions are at or below a permissible limit, the current estimated feature positions are taken as the real feature positions.
Meanwhile, if the differences between the initial estimated feature positions and the comparison feature positions are larger than the permissible limit, the current estimated feature positions are replaced with new estimated feature positions given by correcting the current estimated feature positions by values according to the differences. After that, until the differences between the initial estimated feature positions and the comparison feature positions, i.e. the differences between the current estimated feature positions and the real feature positions, become at or below the permissible limit, the calculating of image information, the calculating of image information, the calculating of comparison feature positions, and the correcting and updating of the current estimated feature positions are repeated. And when the differences between the initial estimated feature positions and comparison feature positions become at or below the permissible limit, the current estimated feature positions are taken as the real feature positions.
Therefore, according to the position detecting method of this invention, even when cross-talks are present between a plurality of features in an image formed on the image plane, the real positions of the plurality of features can be detected accurately.
In the position detecting method of this invention, the predetermined optical system may include a micro-lens array in which lens elements are arranged in a matrix.
Moreover, in the position detecting method of this invention, the specific algorism may be one of a center-of-gravity method and correlation method.
Yet further, in the position detecting method of this invention, the feature may be a spot.
According to a second aspect of the present invention, there is provided an optical characteristic measuring method with which to measure an optical characteristic of an optical system to be examined, the optical characteristic measuring method comprising dividing a wave front of light which has passed through the optical system to be examined, by a predetermined optical system to form an image having a plurality of features; picking up the image having the plurality of features; detecting positions of the plurality of features in the image using the position detecting method according to this invention; and calculating an optical characteristic of the optical system to be examined based on the detected positions of the plurality of features.
According to this, the positions of the plurality of features in the image formed on the image plane are accurately detected using the position detecting method according to this invention. Based on the detected positions of the plurality of features, the optical characteristic of the optical system to be examined is calculated. Accordingly, the optical characteristic of the optical system can be very accurately measured.
In the optical characteristic measuring method according to this invention, the optical characteristic may be wave-front aberration.
According to a third aspect of the present invention, there is provided an optical characteristic measuring unit which measures an optical characteristic of an optical system to be examined, the optical characteristic measuring unit comprising a wave-front dividing device which is arranged on an optical path of light passing through the optical system to be examined, divides a wave front of the light passing through the optical system to be examined, and forms an image having a plurality of features; a pick-up unit which is arranged a predetermined distance apart from the wave-front dividing device and picks up the image having the plurality of features; a position detecting unit connected to the pick-up unit, which detects positions of the plurality of features in the image using the position detecting method according to this invention with the wave-front dividing device as the predetermined optical system; and an optical characteristic calculating unit connected to the position detecting unit, which calculates an optical characteristic of the optical system to be examined based on the detected positions of the plurality of features.
According to this, a pick-up unit picks up an image having a plurality of features that is formed through a wave-front dividing device. Subsequently, a position detecting unit using the position detecting method of this invention accurately detects the positions of the plurality of features from the pick-up result. And an optical characteristic calculating unit calculates the optical characteristic of the optical system to be examined based on the detected positions of the plurality of features. That is, the optical characteristic measuring unit of this invention measures the optical characteristic of the optical system to be examined using the optical characteristic measuring method of this invention, so that the optical characteristic of the optical system can be accurately measured.
In the optical characteristic measuring unit according to this invention, the wave-front dividing device may be a micro-lens array in which lens elements are arranged in a matrix.
Moreover, in the optical characteristic measuring unit according to this invention, the optical system to be examined may be a projection optical system that transfers a pattern formed on a mask onto a substrate.
Here, a housing that houses the wave-front dividing device and the pick-up unit may be attached to a stage that holds the substrate.
According to a fourth aspect of the present invention, there is provided an exposure apparatus which, by illuminating a substrate with exposure light, transfers a predetermined pattern onto a substrate, comprising an exposure apparatus main body which comprises a projection optical system arranged on an optical path of the exposure light; and an optical characteristic measuring unit according to this invention with the projection optical system as the optical system to be examined.
According to this, a given pattern is transferred on a substrate by a projection optical system of which the optical characteristic has been measured accurately by the optical characteristic measuring unit of this invention and adjusted suitably. Therefore, the given pattern can be very accurately transferred on the substrate.
In the exposure apparatus according to this invention, the optical characteristic measuring unit may be attachable to and detachable from the exposure apparatus main body.
According to a fifth aspect of the present invention, there is provided a device manufacturing method including a lithography process, wherein in the lithography process, an exposure apparatus according to this invention performs exposure. According to this, because the exposure apparatus of this invention can very accurately transfer a given pattern onto divided areas, productivity in manufacturing highly integrated devices having a fine circuit pattern can be improved.